Classical and Discrete Functional Analysis with Measure Theory
Classical and Discrete Functional Analysis with Measure Theory
$55.00
USDFunctional analysis deals with infinite-dimensional spaces. Its results are among the greatest achievements of modern mathematics and it has wide-reaching applications to probability theory, statistics, economics, classical and quantum physics, chemistry, engineering, and pure mathematics. This book deals with measure theory and discrete aspects of functional analysis, including Fourier series, sequence spaces, matrix maps, and summability. Based on the author's extensive teaching experience, the text is accessible to advanced undergraduate and first-year graduate students. It can be used as a basis for a one-term course or for a one-year sequence, and is suitable for self-study for readers with an undergraduate-level understanding of real analysis and linear algebra. More than 750 exercises are included to help the reader test their understanding. Key background material is summarized in the Preliminaries.
- Keeps prerequisites to a minimum and is accessible to those with undergraduate-level knowledge of real analysis and linear algebra, including students in physics and engineering
- Contains 760 exercises to test and develop understanding
- Suitable for self-study or as a basis for two independent one-term courses or for a one-year sequence
- Has applications to many areas, including probability, statistics, approximation theory, classical physics, quantum mechanics, wavelets, and signal processing
Reviews & endorsements
'Every theorem, proposition, lemma, and corollary has a very understandable proof, is easy to follow, and is well supported by the previous results (in the sense of a self-contained book). … I do not hesitate to say that this book is not far from being an encyclopedic book in functional analysis-measure theory-Fourier series.' Rigoberto Vera Mendoza, MathSciNet (https://mathscinet.ams.org)
Product details
January 2022Paperback
9781107634886
350 pages
230 × 152 × 28 mm
0.72kg
Not yet published - available from May 2025
Table of Contents
- Preliminaries
- Part I. Measure and Integration:
- 1. Lebesgue measure
- 2. Lebesgue integral
- 3. Some calculus
- 4. Abstract measures
- Part II. Elements of Classical Functional Analysis:
- 5. Metric and normed spaces
- 6. Linear operators
- Part III. Discrete Functional Analysis:
- 7. Fourier series
- 8. Applications
- 9. Sequence spaces
- 10. Matrix maps, multipliers, and duality
- 11. Summability
- Index.
